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# If a = c*10^b and a and b are integers, what is the value of b?

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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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02 Oct 2017, 23:57
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If a = c*10^b and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
(2) 1 < b < 4

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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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Updated on: 15 Oct 2017, 02:00
1
Bunuel wrote:
If a = c*10^b and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
(2) 1 < b < 4

Statement 1: $$c=0.xyz$$, where $$x,y,z$$ are digits in tenths, hundredths, and thousandths places but nothing mentioned about $$a$$ or $$b$$. Hence $$insufficient$$

Statement 2: $$b$$ can be $$2$$ or $$3$$. Hence insufficient

Combining 1 & 2. $$a = c*10^b$$,

or $$a= 0.xyz*10^b$$ we know that $$a$$ is an integer, hence $$b=3$$ because if $$b=2$$ then $$a=xy.z$$ which is not an integer. Hence sufficient

Option C

Originally posted by niks18 on 03 Oct 2017, 02:20.
Last edited by niks18 on 15 Oct 2017, 02:00, edited 2 times in total.
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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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03 Oct 2017, 02:39
If $$a = c*10^b$$and a and b are integers, what is the value of b?

(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.
=> This tells us that c is a 3 digit decimal number => c = 0.pqr ( p,q,and r are single digit integers)

to make 'a' as an integer 'c' need to be multiplied by 1000 => minimum value of a => $$a = c*10^3$$
Here as we don't know value of a => b can take any value greater or equal to 3 => $$b\geq{3}$$
Insufficient

(2) 1 < b < 4
as b is an integer => b = 2 or 3
Insufficient

1+2

=>by statement 1=> $$b\geq{3}$$
by statement 2 => b = 2 or 3
=> b=3

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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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03 Oct 2017, 07:01
(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?
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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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03 Oct 2017, 07:12
kunalsinghNS wrote:
(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?

Hi kunalsinghNS

it is mentioned in the statement that ONLY tenths, hundredths, and thousandths places have non zero digits
So $$c=0.234$$ or $$c=10.897$$. In either case if you multiply $$c$$ by $$10^3$$, then it will become an integer
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If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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03 Oct 2017, 08:54
kunalsinghNS wrote:
(1) c has nonzero digits in only the tenths, hundredths, and thousandths places.

How come you can deduce that "C" is a decimal digit ?

Please refer attached figure and below mentioned line, it might help.

c has nonzero digits in only the tenths, hundredths, and thousandths places.
Attachments

Number.jpg [ 16.72 KiB | Viewed 784 times ]

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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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03 Oct 2017, 19:53
Thank you for the explanation niks18 and Nikkb
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Re: If a = c*10^b and a and b are integers, what is the value of b?  [#permalink]

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29 Mar 2018, 02:11
It will help if you catch the difference
tens-tenth
hundreds - hundredth
thousands - thousandth
Re: If a = c*10^b and a and b are integers, what is the value of b? &nbs [#permalink] 29 Mar 2018, 02:11
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